William F. Browder was one of the most prominent foreign investors here, a corporate provocateur who brought the tactics of Wall Street shareholder activists to the free-for-all of post-Soviet capitalism. Until, that is, the Kremlin expelled him in 2005.

Mr. Browder then focused on protecting his billions of dollars of stakes in major Kremlin-controlled companies, like Gazprom, and on fighting to return to a land where he had deep and unusual family ties. So when he ran into Dmitri A. Medvedev, the country’s future president, at the World Economic Forum in Davos last year, he saw his chance.

In a brief conversation at a dinner at the Swiss resort, he pressed Mr. Medvedev for help in regaining his Russian visa. Mr. Medvedev, then a top aide to President Vladimir V. Putin, agreed to pass along his request.